Modigliani-Miller Theorem
Under some assumptions, corporate financial policy is
IRRELEVANT.
• Financing decisions are irrelevant.
• Capital structure is irrelevant.
• Dividend policy is irrelevant.
• Cash management is irrelevant.
• Risk management policy is irrelevant.
• Cross shareholdings are irrelevant.
• Diversification is irrelevant.
• Etc.
The Original Propositions
• MM-Proposition I (MM 1958)
A firm’s total market value is independent
of its capital structure.
• MM-Proposition II (MM 1958)
A firm’s cost of equity increases with its
debt-equity ratio.
• Dividend Irrelevance (MM 1961)
A firm’s total market value is independent
of its dividend policy.
• Investor Indifference (Stiglitz 1969)
Individual investors are indifferent to the
firms’ financial policy.
Assumptions
• Frictionless markets: No transaction costs, etc.
• Competitive markets: Individuals and firms are pricetakers.
• Individuals and firms can undertake financial transactions at the same prices (e.g., borrow at the same
rate).
• All agents have the same information.
• No taxes.
• A firm’s cashflows do not depend on its financial policy
(e.g., no bankruptcy costs).
MM as a No-Arbitarge Argument
• Value additivity:
– No arbitrage Profits in Equilibrium
– Value additivity: If A and B are cashflow streams,
no arbitrage =⇒
V (A + B) = V (A) + V (B) .
• Firm value:
– A firm’s value ≡ the sum of the values of all its
financial claims.
– The cashflows received by all its claims must add
up to the total cashflow that assets generate.
– Value additivity. ⇒ The firm’s value must equal
that of the assets’ cashflow stream.
• Identical firm:
– Consider an identical firm with a different financial
policy.
– Assets being identical, they generate the same
cashflow stream. ⇒ Firm value is the same.
Model
2 Firms: 1, 2
• At t = 1, 2, ..., both firms yield the same (random)
CF X.
• At t = 0, they have different capital structures:
– Firm 1 has equity and a constant level of risk-free
debt.
– Firm 2 has no debt.
• At t = 0,
– Risk-free rate: r.
– Market value of firm i’s debt: Di.
– Market value of firm i’s equity: Ei.
– Total market value of firm i: Vi = Di + Ei.
• Hence, at t:
– Firm 1’s debtholders receive: rD1.
– Firm 1’s equityholders receive: X − rD1.
– Firm 2’s equityholders receive: X.
Step 1: It cannot be that V2 > V1.
• Suppose V2 > V1.
• An investor could:
– Short sell a fraction α of firm 2’s shares for αV2.
– Use the proceeds to buy a fraction αV2/V1 of firm
1’s debt and equity as:
αV2 
αV2 
αV2 = 
· D1 + 
· E1.
V1
V1




• At t, the investor would receive:
αV2 
αV2 
rD1 + 
· (X − rD1)
−αX + 
V1
V1


V
2
= α −1 +  X > 0
V1
for all X.




• ⇒ An arbitrage opportunity exists.
• Intuition: Arbitrageurs can “undo firm 1’s leverage” by buying equal proportions of its debt and equity
so that interest paid and received cancel out.
Step 2: It cannot be that V1 > V2.
• Suppose V1 > V2.
• An investor could:
– Short sell a fraction α of firm 1’s shares for αE1.
– Borrow αD1.
– Use the proceeds to buy a fraction αV1/V2 of firm
2’s shares as:


αV
1
·V .
αE1 + αD1 = 
2
V2
• At t, the investor would receive:get α
interests rαD1:
V1
X and pay
V2
V1
αV1 
X = α −1 +  X > 0
−α (X − rD1) − rαD1 + 
V2
V2
for all X.



• ⇒ An arbitrage opportunity exists.
• Intuition: Arbitrageurs can “lever up” firm 2 by
borrowing on individual accounts (homemade leverage).

MM and the Cost of Capital
Proposition II: A firm’s cost of equity increases
with its debt-equity ratio.
• Intuition: Raising debt makes existing equity more
risky, hence more costly.
• Note: Debt makes equity riskier even if it is riskfree,
i.e., this is not (only) about default risk.
• Use the notion of a firm’s WACC
Proof:
• The firm’s Weighted Average Cost of Capital (WACC)
is:
E
D
r+
rE
WACC =
D+E
D+E
where:
– r is the cost of risk-free debt, i.e., its return.
– rE is the cost of equity, i.e., its expected return.
• This can be rewritten as:
rE = (WACC − r)
D
+ WACC.
E
• By Proposition I, the WACC is independent of D/E.
⇒ rE is linear in D/E.
• Note:In practice, WACC > r (i.e., rE > r) essentially
for all firms. ⇒ rE increases with D/E.
But we all know that debt is cheaper than equity —• Isn’t debt cheaper than equity?
– Interest rates on corporate debt ' 5%.
– Equity earnings/price ratios (then the conventional
measure of the cost of equity capital) ' 20%.
• MM’s Proposition II shows that there is no contradiction.
• By issuing debt at 5% the firm would increase the
riskiness of equity.
• Difference between rE and r is irrelevant!
But, some people value dividend streams.
Financial Structure does matter
• Heterogenous investors value the same cash flow streams
differently.
• ⇒ Financial policy choices affect the match between
securities and heterogenous preferences.
• ⇒ Financial policy can affect firm value.
Argument: An all-equity firm doesn’t exploit the demands for risky and safe securities.
It may be worth more by separating riskier from safer cash
flow streams (e.g., into debt and equity) so that investors
can focus on their preferred security.
Intuition for MM:
• MM show that this theory is flawed (Win-Win Fallacy).
• Investors’ preferences are over cashflows, not securities.
• They are not limited to the securities issued by firms.
• If investors can trade at the same prices as firms, they
won’t pay a premium for the firm to trade for them.
• MM do not assume away heterogeneity.
• The match between preferences and cash flow streams
need not be organized by the firms.
• There is no value to financial marketing.
MM DIVIDEND POLICY IRRELEVANCE
Proposition: A firm’s value is independent of
its dividend policy.
• Each “period”, the firm:
– Invests and retains cash (Investment Policy).
– Raises new capital (Financing Policy).
– Pays some dividends (Payout Policy).
• Accounting identity: Taking investment as given, a
change in payout has to be met by a change in financing.
• For instance:
– A dividend increase can be financed with a new
debt issue.
– A dividend decrease can be met by a retirement
of debt.
• Existing shareholders and new investors form a “closed
system”.
⇒ The total value of their claims is unaffected (value
conservation).
• New investors are competitive.
⇒ The value of their claims is unchanged.
⇒ The value of the current shareholders’ claims is
unchanged.
Important because....
• For the study of dividend policy:
– Why do firms pay dividends?
• For the other MM propositions:
– The arbitrage proof relies on firms generating identical cashflows.
– But shareholders receive dividends, not cashflows.
– Do dividends have to be identical too?
Another Argument........
Dividends are safer than future payments. ⇒ Don’t they
increase firm value?
• MM show that this theory is flawed
USING MM SENSIBLY
• Financial decisions do matter.
• So what do we make of the irrelevance result?
– Avoid the fallacies
– Organize your thoughts.
Main insight:
• Value is created only by real assets
• If Financial Policy is unrelated to Investment Policy,
then it is irrelevant: It merely divides a “pie” of fixed
size.
• Serves as a benchmark: If we know what does not
matter, we may be able to infer what does.
How can financial decisions affect the size of
the pie?
• Investors cannot undertake the same financial transactions as firms
– Taxes,
– transaction costs and short-sale constraints,
– bankruptcy costs,
– information asymmetries,
– Moral hazard
The Static Tradeoff Theory
Main idea:
• Capital structure matters because:
– Debt has a tax advantage over equity.
– Debt involves bankruptcy costs.
• Trade-off. ⇒ Optimal capital structure (firmspecific).
DEBT TAX SHIELD
• At the corporate level:
– Interest payments are tax deductible.
– Dividends and retained earnings are taxed.
• Consider a firm that:
– generates cashflow X in t = 0, 1, 2...
– has a constant level of riskfree debt D.
• Notation:
– Riskfree rate: r.
– Corporate tax rate: τ .
• Each period, the after tax cashflow is:
|
(1 − τ ) (X
− rD)
{z
to equityholders
+
}
rD
{z
}
to debtholders
|
• Rewrite as:
(1 −{zτ ) X } +
all equity firm
|
τ rD
{z
}
tax shield
|
Proposition (MM with corporate taxes):
• The value of a levered firm equals that
of an unlevered firm plus that of the interest tax shield.
• Here:
V (D) = V (0) + τ D.
Proof:
• By value additivity:
V (D) = V (0) + V (Tax Shield Perpetuity).
• Moreover, the value of the tax reduction is:
V (Tax Shield Perpetuity) =
τ rD
= τ D.
r
• Intuition: In effect, the government pays a fraction
τ of the interest. Investors cannot get such a tax
break on homemade leverage. Hence, they will pay a
premium for levered firms.
• Note: If the government’s tax claim is included, MM
Proposition I holds: Firm Value+V (Taxes) is independent of capital structure.
BANKRUPTCY COSTS
• Debt implies a risk of bankruptcy.
• Bankruptcy costs:
– Administrative and court cost, legal and advisory
fees.
– Resources spent by management and creditors dealing with bankruptcy.
– Mismanagement by judges (blocking/delaying nonroutine expenditures).
– In US, average time spent in bankruptcy: 20 months.
• Note: This violates the MM assumption that cashflows are independent of financial policy.
STATIC TRADE-OFF THEORY
• As leverage increases:
– Tax shield increases.
– Expected bankruptcy costs increase:
∗ Probability of bankruptcy increases.
∗ Costs when in bankruptcy increase (most likely).
• Optimal leverage (ratio) trades-off these costs and
benefits.
• Remarks/Implications:
– Optimal leverage should be firm-specific.
– Static trade-off: Observed capital structures should
be close to the target, hence relatively stable.
– This contrasts with other theories of capital structure.
– As firms strive to approach a target capital structure, we might observe mean-reversion (to the target).
ISSUES
The tax effect can be substantial.
• Consider a firm with constant riskfree cash flow X:
V (100%) = V (0%) + τ V (100%)
V (0%)
⇒
= 1 − τ ' 60%.
V (100%)
• Note: Many firms’ effective tax rate is below the
statutory tax rate due to tax credits, etc.
• Therefore, tax effect’s order of magnitude is much
lower.
Direct bankruptcy costs are generally too
small to offset the potentially big tax gains.
• Direct bankruptcy costs can amount to $100Ms, but
should be compared to firm value.
• Large firms: Small fraction of firm value when entering bankruptcy (e.g. 5%, see Warner (1977), Weiss
(1990)).
• Smaller firms: Higher fraction (e.g., 20%).
• These overestimate the relevant cost.
– Need the expected cost as a fraction of firm value
at the time when capital structure is decided.
– Caveat 1: Firm value is low near bankruptcy. ⇒
5% is an overestimate.
– Caveat 2: Ex-ante distress probability is small.
⇒ For many firms, STO suggest that high
leverage is optimal.
⇒ Firms tend to be less leveraged than predicted by STO.
⇒ Does not count growth options
PERSONAL TAXES
Main idea: For personal taxes, equity has an
advantage over debt.
• Classical tax systems: (e.g., US).
– Interests and dividends are taxed as ordinary income.
– Capital gains are taxed at a lower effective rate:
∗ Sometimes, lower tax rate
∗ Capital gains can be deferred (6= dividends and
interests). ⇒ Earn the time value.
– However, some dividend exclusion (e.g. 70%) for
corporations.
• Imputation systems: (e.g., most of Europe).
– Tax credits for recipients of dividends (= fraction
of corporate tax) reduce the double taxation of
dividends.
• At the personal level:
– Tax rate on debt: τD .
– Tax rate on equity (dividend + capital gains): τE .
• Each period, the cashflow after corporate and personal
taxes is:
− τ{zD ) rD}
(1
− τE ) (1 −{zτ ) (X − rD)} + (1
|
|
to debtholders
to equityholders
• Rewritten as:
(1
− τE ) {z(1 − τ ) X} + |[(1 − τD ) − (1 −{z τE ) (1 − τ )] rD}
|
all-equity firm
tax impact of debt
Proposition (MM with corporate and personal
taxes):


(1 − τ ) (1 − τE ) 
 D.
V (D) = V (0) + 1 −
(1 − τD )
Debt vs. Equity
• Debt tax shield:
(1 − τ )(1 − τE )
.
1 − τD
• Effective τE increases with the payout ratio.
• If τD ' τE (e.g. equity pays large dividends):
– We can ignore personal taxes.
– We are back to MM with corporate taxes
V (D) = V (0) + τ D.
– Debt has a strong tax advantage over equity.
• ⇒ Dividend Puzzle: Tax-disadvantage relative to debt
and capital gains.
• If τE < τD (e.g. equity can avoid large dividends):
– Equity does not look as bad.
– Debt’s tax shield is less than τ D.
• If
(1−τ )(1−τE )
1−τD
> 1:
– Debt has a negative tax shield.
– Equity has a tax advantage over debt.
THE MILLER EQUILIBRIUM
Miller (1977).
• Capital structure is:
– Uniquely determined at the aggregate
level.
– Irrelevant at the firm level.
• With τE = 0 (for simplicity), a firm prefers debt to
equity iff τ > τD .
• If all firms face the same τ and all investors the same
τD , all firms issue the same claim, i.e., no debt-equity
mix.
• Assume instead investors with heterogenous personal
tax rates τDi .
• Additional assumptions:
– Firms’ cashflow is certain (debt is riskfree).
– No short sales.
• Yield on tax-exempt (e.g., municipal) bonds: r0.
Demand for corporate debt:
• Investors can always buy tax-exempt bonds offering a
return r0.
– For r < r0, no investor wants corporate debt.
– For r = r0, tax-exempt institutions hold corporate
debt (horizontal stretch).
– For r > r0, tax-paying investor i holds corporate
debt iff:
r0 ≤ 1 −
τDi
r.
Supply of corporate debt:
1
• Paying a return r0 to equityholders costs firms r0 (1−τ
).
1
– For r > r0 (1−τ
) , firms issue no debt, only equity.
1
– For r < r0 (1−τ
) , firms issue only debt, no equity.
1
– For r = r0 (1−τ
) , firms are indifferent between issuing debt and equity (⇒ Perfectly elastic supply).
Equilibrium:
• There are gains from trade (i.e., from issuing debt)
until the marginal investor’s tax rate is τDm = τ .
• If the debt supply exceeded D∗, r would be driven
1
∗
above r0 (1−τ
) , and vice versa if less than D were
issued.
Implications
• Capital structure is irrelevant at the firm
level:

V (D) = V (0) + 1 −

(1 − τ ) 
 D = V (0).
m
(1 − τD )
• Unique aggregate debt-equity ratio: In equilibrium, aggregate debt is such that the marginal investor is indifferent between debt and equity, i.e.,
(1 − τDm) = (1 − τ ).
• The equilibrium aggregate debt level depends on:
– Tax rates.
– Funds available to investors in each tax bracket.
• Clientele effect:
– Investors with τD > τDm hold only equity and taxexempt bonds.
– Investors with τD < τDm hold only corporate bonds.
Relevance
• This is plausible only if the effective personal tax rate
on equity is substantially lower than rate on interest.
• Although τE < τD , corporate tax advantage of debt
seems to exceed personal tax disadvantage for most
investors,
• i.e., Aren’t many investors with
(1 − τD ) < (1 − τ )(1 − τE )
• No strong clientele effect:
– Highly taxed individuals do not only hold equity.
– Tax-exempt institutions do not only invest in corporate bonds.
NON-DEBT TAX SHIELDS
• Many firms cannot fully exploit the tax deductibility
of interests because of:
– Negative earnings (EBITDA).
– Non-debt tax shields: Depreciation, tax credits,
etc.
• Tax Loss Carry Forwards (TLCF):
– Several years, but most firms continue to have
losses for several years.
– ⇒ They lose the time value of the debt tax shield.
• Implication:
– Other things equal, the expected tax rate decreases
with leverage.
– The marginal debt tax shield decreases
with leverage.
BOTTOM LINE
• Taxes favor debt for most firms, but beware of particular cases.
• It is still standard to use τ D to evaluate the debt tax
shield.
• Somewhat overstated.
• Definitely NOT OK for non-tax paying firms.
MODELS BASED ON INCENTIVE
PROBLEMS
• Moral hazard.
• Moral hazard and credit rationing.
• Jensen and Meckling (1976).
– Effort problem.
– Risk-shifting problem.
INCENTIVE ISSUES
Main idea:
• Conflicts of interests between the party making operating decisions (≡ insider) and outside investors.
• Outside financing involves costs due to Moral
Hazard:
– Deviations from value maximization.
– Credit rationing: Some valuable projects
cannot be financed.
– Costs incurred to prevent the above such
as:
∗ Monitoring
∗ Bonding.
• Role for internal funds.
Model
• Three dates (t = 0, 1, 2), no discounting, and universal risk-neutrality.
• An entrepreneur has a project.
• At t = 0: Financing.
– Needs to invest I > 0.
– Entrepreneur’s resources available: W .
• At t = 1: Moral hazard.
– The entrepreneur is key to the project.
– He can choose an “effort” level e ∈ {0, 1}.
– Cost c (0) = 0 and c(1) = c.
• At t = 2: Cash flow.
L
– X ∈ X ,X
H
– and Pr X = X
with ∆X ≡ X H − X L > 0,
H
≡ θ + e · ∆θ .
Assumption (*): e = 1 is efficient, i.e.,
∆θ ∆X > c.
Assumption: The project’s value is positive if e = 1,
i.e.,
V1 ≡ X L + (θ + ∆θ ) ∆X − I − c > 0.
• “Effort” is a metaphor
• The incentives of the party taking operating decisions
depends on his claims.
• Therefore, the pie size is affected by how it is split.
⇒ Violates one MM assumption.
Financial Contracts
• Financial claims are promises of payments at t = 2,
contingent on X:
RL if X = X L and RH ≡ RL + ∆R if X = X H .
• Limited liability:
RL ≤ X L and RH ≤ X H
Examples:
• Debt with face value K:
RL = min{X L, K} and RH = min{X H , K}.
• Fraction β of equity:
RL = βX L and RH = βX H .
• Call option on the firm’s equity with strike K:
RL = max{X L − K, 0} and RH = max{X H − K, 0}.
• Etc.
Remark:
• If X L = 0, all contracts are linear (in cashflows):
RL = 0 and RH ≥ 0.
• There is no difference between debt, equity, etc.
• Useful modelling trick when one wants to concentrate
on internal vs. external finance as opposed to the type
of external finance.
First Best
If W ≥ I, the entrepreneur should:
• Invest I and exert e = 1.
What if W < I?
• The entrepreneur needs to raise at least (I − W ).
• He can sell a claim (RL, RH ).
• Competitive investors are willing to pay
RL + (θ + ∆θ )∆R .
Assumption (for now): X L = 0.
• The entrepreneur raises at least (I − W ) with a claim
such that:
I −W
H
RH ≥ Rmin
≡
.
θ + ∆θ
H
• Note: Possible since Rmin
≤ XH.
• For instance, he can sell a claim to the entire cash
flow, i.e., RH = X H .
• Irrespective of W , the entrepreneur can always finance
the project.
• MM applies: Firm value is independent of whether
and how much the project if funded internally vs. externally.
• True if there is no incentive problem, i.e., effort is
contractible or not costly.
Moral Hazard
Assumption: Effort is costly (i.e., c > 0) and noncontractible.
• conflict + non-contractibility creates an incentive problem.
• For instance:
– Suppose that the entrepreneur sells the entire cashflow at t = 0.
– He has no incentives to incur a cost c(e) > 0 at
t = 1.
– Investors are willing to pay less for the firm’s claims.
• At t = 1, the entrepreneur chooses e = 1 iff:
∆θ (X H − RH ) ≥ c
or
H
RH ≤ Rmax
≡ X H − c/∆θ .
• But financing the project (given e = 1) requires:
H
RH ≥ Rmin
≡ (I − W )/(θ + ∆θ ).
• Hence, the first best is obtained iff:
H
H
Rmin
≤ Rmax
.
Note: If the entrepreneur were not key to the project,
he could sell it to an investor who would run the project
(i.e., choose e).
Implications
• Role of internal funds:
– The condition is more likely to be satisfied when
W is large.
– Firms with more internal funds are less constrained
in their investment policy.
H
H
?
> Rmax
What if Rmin
• The project’s value for e = 0 is:
V0 ≡ X L + θ∆X − I.
• Credit rationing:
– Suppose V0 < 0.
– The entrepreneur cannot raise (I − W ), irrespective of RH .
• Deviation from value maximization:
– Suppose V0 > 0.
– The entrepreneur can raise (I − W ) but fails to
use these funds optimally.
Commitment Problem
• The entrepreneur’s payoff is:
Firm value − Net
payment to competitive
investor(s)} .
|
{z
=0
⇒ He is best-off maximizing firm value, so e = 1.
• Ultimately, the entrepreneur bears the costs of moral
hazard.
• However, once some claims are sold to investors, his
incentives are determined only by the claims that he
retains.
Costly commitment:
• To commit to e = 1, the entrepreneur is willing to pay
up to:
V1 − max{V0, 0}.
• Monitoring by a blockholder, a bank, an auditor,
etc...
• Bonding: Contractual commitment not to take certain actions (even if potentially valuable): Loan earmarking, etc.
Important Remark: Effort is a Metaphor
• The entrepreneur allocates the firm’s resources (including but not only his labor) between activities generating:
– Security benefits, accruing to the firm’s claimholders,
– Private benefits, accruing to the entrepreneur
only.
• Note: Private benefits are negative private costs.
⇒ c(e) is the entrepreneur’s opportunity cost of not
getting private benefits.
⇒ Effort is efficient. ⇔ Private benefits are inefficient.
Examples:
• Future investment/funding decisions (Debt overhang).
• Empire building: Managers like large firms. Power?
Insurance?
• Entrenchment activities (Shleifer and Vishny 1989).
• Career concerns.
• Sustain family control (Is managerial talent hereditary?).
• Perks, pet projects, etc. (Nabisco)
• Assets sold in sweetheart deals or for window dressing.
• “Time”: Work versus golf or outside jobs.
CAPITAL STRUCTURE
Jensen and Meckling (1976).
Main idea:
• Conflicts of interests:
– Between inside and outside equityholders.
– Between equityholders and debtholders.
• Specific costs:
– Outside equity ⇒ Low “effort.”
– Debt ⇒ Risk-shifting (aka asset substitution).
• Optimal capital structure minimizes these
agency costs.
Model
Same as before except:
• X L > 0, to be able to discuss financing choices.
• I > X L, for simplicity.
• W = 0, for simplicity.
First-Best: Modigliani-Miller
• Financing choices are irrelevant in the absence of Moral
Hazard (i.e., if c = 0 or e is contractible).
• Say the entrepreneur chooses to raise exactly:
I = RL + (θ + ∆θ ) ∆R .
I − XL
• He can issue debt with face value K = X +
,
θ + ∆θ
i.e.,
L
RL = min{X L, K} = X L
RH = min{X H , K} = K.
• Alternatively he can issue equity: Sell a fraction
β=
I
X L + (θ + ∆θ )∆X
of existing shares, i.e.,
RL = βX L
RH = βX H .
• Intuition: Competitive investors. ⇒ Irrespective of
financing, the entrepreneur receives the project’s entire value.
Optimality of Debt
• At t = 1, the entrepreneur chooses e = 1 iff:
∆θ (∆X − ∆R ) ≥ c
or
∆R ≤ ∆max
≡ ∆X − c/∆θ .
R
• Debt is the contract making this constraint least severe, i.e., binding for a smallest set of parameters as,
it solves:
min ∆R
(RL ,RH )
RL ≤ X L
RH ≤ X H
I ≤ RL + (θ + ∆θ ) ∆R
• Debt is an optimal response to the effort problem:
Projects that can be funded (e.g., with equity) can
also be debt financed but the reverse is not true.
• Intuition: The optimal (debt) contract maximizes
the fraction of the return from effort that accrues to
the entrepreneur. Hence, it maximizes his incentive to
exert effort.
Cost of Debt: “Risk-Shifting”
• Same model except for Moral hazard at t = 1.
• Two mutually exclusive projects generating X ∈ {0, X̂, 2X̂}
at t = 2.
Pr[X = 2X̂] Pr [X = 0]
Project A:
θ1
θ2
Project B:
θ 1 + ∆1
θ 2 + ∆2
with 0 < ∆1 < ∆2 and θ1 + ∆1 + θ2 + ∆2 < 1.
• Assume that Project A’s value is positive, i.e.,
(1 + θ1 − θ2)X̂ − I > 0.
First Best
• Project B’s value is
(1 + θ1 + ∆1 − θ2 − ∆2)X̂ − I.
• This is less than Value(Project A), the difference being:
(∆2 − ∆1)X̂ > 0.
• ⇒ I should be used for Project A.
Debt Finance?
• Suppose that I is raised in debt with face value K.
• Assume (for simplicity) that K > X̂, i.e.,
(1 − θ2)X̂ < I.
• The entrepreneur gets a positive payoff only when
X = 2X̂.
• With Project A, he gets:
θ1(2X̂ − K).
• With Project B, he gets:
(θ1 + ∆1)(2X̂ − K).
⇒ Once I has been raised, the entrepreneur picks
Project B.
Equity Finance?
• Suppose I has been raised in equity.
• Once I raised and invested, the entrepreneur gets a
fixed share of cash flows.
• ⇒ He maximizes expected cash flows.
• ⇒ He undertakes Project A.
• Equity is optimal since it induces no distortion in investment.
Intuition
• The difference between Project A and Project B has
two parts.
• An increase in θ1 and θ2 by ∆1 which preserves the
mean:
∆12X̂ − 2∆1X̂ + ∆1 · 0 = 0
but increases the variance.
• An increase in θ2 by (∆2 − ∆1) which decreases the
mean:
−(∆2 − ∆1)X̂ + (∆2 − ∆1) · 0 < 0.
Debt:
• Risky debt’s payoff is concave in cash flows.
⇒ Levered equity’s payoff is convex in cash flows.
⇒ Equityholders have an incentive to take excessive
risk.
• Value of call option increases with volatility. ⇒ Riskshifting problem.
Equity:
• The entrepreneur and the investors have the same
claims. ⇒ No conflict.
• Linear claims. ⇒ No risk-shifting.
• Note: Equity dominates debt but also all other contracts. This holds in more general models (see Green
1984).
Extension to Managerial Firms?
• The model fits entrepreneurial firms.
• Can we extend it to large firms in which many key decisions are taken by employed professional managers?
• Does it provide a theory of capital structure for such
firms?
No:
• The effort model is useful for managerial firms only
if managers are not a priori indifferent to the firm’s
operating decisions.
• At best, a theory of managerial compensation, not
capital structure.
Extension to Managerial Firms?
• The literature happily applies the theory also (and in
fact primarily) to managerial firms.
• That is, it presents all firms as being entrepreneurial
but derives implications for managerial firms.
• This requires a non-standard assumption about managerial behavior:
Assumption: Managers act in the interest of shareholders.
• Otherwise, the problem could be solved by a contract linking managerial compensation to the entire
firm value rather than, e.g., the value of the existing
equity (Dybvig and Zender 1991).
• “Coherent” interpretation: Only existing shareholders
can sign secret contracts with managers, i.e., undo
the optimal contract (Persons 1994).
• But why?
• With these caveats in mind, the analysis goes through
unchanged. (In fact, there is no scope for risk-shifting
with equity finance, i.e., the problem does not even
arise since managers serve all shareholders).
• In fact, in entrepreneurial firms, risk-neutrality may
not be a compelling assumption. The entrepreneur
may be bearing a lot of idiosyncratic risk. Hence, he
might take too little risk?
Risk-Shifting Model’s Implications
• More debt when there is less risk-shifting potential:
e.g.,
– Regulated public utilities with less managerial discretion (Bradley, Jarrell and Kim 1984).
– Firms in mature industries with few growth opportunities (Barclay, Smith and Watts 1992).
• Risk shifting incentives are higher in financial distress
because limited liability kicks in (“Gambling for Resurrection”).
• For instance, managers may delay filing for bankruptcy
to keep equity’s option value alive.
• Or they may file for Chapter 11 rather than Chapter
7.
Mitigating asset substitution:
• Covenants to debt contract, e.g., interest coverage
requirements or prohibition of investments into new,
unrelated lines of business (Smith and Warner 1979).
• Convertible debt alleviates existing shareholders’
risk-taking incentives by allowing debtholders to share
in the upside, making shareholders’ payoff partly concave (Green 1984).
New Perspective on Capital Structure
• The optimal capital structure minimizes the sum of all
agency costs.
• Hence, the optimal capital structure is likely to be a
mix of debt and equity.
• Note: Jensen and Meckling (1976) study both problems separately. They conjecture that a debt-equity
mix is optimal. In a model including both problems,
new issues arise, e.g., the entrepreneur may try to conceal low effort with high risk choices. Hellwig (1994)
finds that a debt-equity mix is indeed optimal (though
not uniquely so).
• Agency costs include monitoring and bonding costs.
INFORMATION ASYMMETRIES
• Under-diversification (Leland and Pyle 1977).
• Debt as a managerial signal (Ross 1977).
Main ideas:
(1) Information asymmetries between:
• (Some of ) the firm’s existing claimholders.
• New investors.
(2) Outside finance is costly due to asymmetric information:
• Misallocation of funds.
• Credit rationing: Some valuable projects
cannot be financed.
• Costs incurred to prevent the above such
as:
– Monitoring.
– Signalling.
– Etc.
Model
Two dates (t = 1, 2), no discounting
An entrepreneur has the following project:
• At t = 1:
– Need I > 0.
– Entrepreneur’s resources available W < I.
• At t = 2:
L
– Cash flow X ∈ X , X
H
.
– Pr X = X H ≡ θ ∈ {θB , θG}.
– ∆θ ≡ θG − θB > 0.
Notation:
• Investors’ prior ν ≡ Pr [θ = θG] .
• Average θ̂ ≡ θB + ν∆θ .
• The project’s value is: V (θ) = X L + θ∆X − I.
Assumption: The good type’s project is valuable,
i.e., V (θG) > 0.
Assumption (for now): X L = 0.
First Best
• If V (θ) > 0, the entrepreneur should raise funds by
selling claims:
RL = 0 and RH ≤ X H
such that
• For instance,
RL = 0 and RH =
I −W
.
θ
θRH ≥ I − W.
Information Asymmetry
Assumption: Only the entrepreneur knows the actual
θ.
• Absent further information, the investors pay θ̂RH .
• ⇒ Investors would:
– Make money on good firms.
– Lose money on bad firms.
• In other words:
– Good firms would sell underpriced claims.
– Bad ones would sell overpriced claims.
– Good firms would subsidize bad firms.
Remark (Milgrom 1981):
• Soft information: The entrepreneur knows but cannot
prove θ.
• Hard information: He can decide whether to prove θ.
• Only soft information leads to problems:
– Investors assume the worst case given their information.
– ⇒ The entrepreneur always reveals all hard information.
Perfect Bayesian Equilibrium (PBE)
A Perfect Bayesian Equilibrium of this game is defined
as:
H
H
• Strategies: RB
and RG
for the bad and good type
respectively (Convention: RH = 0 means that the
project is not undertaken).
• Beliefs: Investors beliefs following any observed action RH :
H
ν(R ) ≡ Pr θ = θG | R
H
.
H
• Incentive Compatibility Constraints: RB
and
H
RG
are optimal for the bad and good type respectively
given the investors’ beliefs.
• Bayes Rule: Investors’ beliefs are obtained from a
priori distribution and observed actions using Bayes’
H
H
Rule, i.e., for RH ∈ {RB
, RG
}:
Pr (θ = θG) ∩ R
ν(R ) =
Pr [RH ]
H
H
.
Remarks:
• Beliefs are also defined for off-equilibrium moves, i.e.,
H
H
ν(RH ) is defined ∀RH , not only for RG
and RB
.
• Beliefs following an off-equilibrium move are not pinned
H
H
down by Bayes Rule, i.e., for RH ∈
/ {RB
, RG
}, ν(RH )
can take any value.
• To construct equilibria, take ν(RH ) = θB for RH ∈
/
H
H
{RB
, RG
}.
Payoffs
• θ̂(RH ) ≡ Investors’ expectation about θ following action RH :
θ̂(RH ) = θB + ν(RH )∆θ .
• If the project is financed, the entrepreneur’s expected
payoff is:
W
{z
}
Available Wealth
+
H
H
θ̂(R
)
·
R
|
{z
}
Raised from Investors
−
|
+
V {z(θ) }
Firms Actual Value
|
H
θR
{z
}
Claims actual value
|
• This can be rewritten as:
W + V{z (θ)
−
|
}
Ents true worth
|
H
θ − θ̂(R ) RH
{z
IA discount
Note: The discount can be negative.
}
Separating Equilibria with Both Types
Investing
H
H
• If RG
6= RB
, Bayes Rule pins down the investors’
beliefs:
H
H
θ̂(RG
) = θG and θ̂(RB
) = θB .
H
• The bad entrepreneur’s payoff from playing RB
is:
W + V{z(θB )
true worth
|
−
}
|
H
(θB − {zθB ) RB
}
=0
H
, he would get:
• By deviating to RG
|
W + V{z(θB )
true worth
−
}
• ⇒ No such equilibrium.
H
(θ
−
θ
)
R
B
G
G
|
{z
<0
}
Separating Equilibria with Only Bad Types
Investing?
• The bad entrepreneur prefers to invest iff:
W + V (θB ) ≥ W or V (θB ) ≥ 0.
H
• By deviating to RB
, the good entrepreneur would get:
H
H
V (θG) − (θG − θB ) RB
= V (θB ) + (θG − θB )(X H − RB
) ≥ 0.
• ⇒ No such equilibrium.
Separating Equilibria with Only Good Types
Investing
• The bad entrepreneur prefers not to invest iff:
H
V (θB ) + (θG − θB ) RG
≤ 0.
• Moreover, the good entrepreneur needs to raise at
least (I − W ):
H
θG RG
≥ I − W.
• Such a separating equilibrium exists iff:
V (θB ) +
∆θ
(I − W ) ≤ 0.
θG
Stuff
• A necessary but not sufficient condition is V (θB ) < 0.
Otherwise, bad entrepreneurs prefer investing.
• The condition is more likely to be satisfied when bad
entrepreneurs then have to bear a larger fraction of
their project’s negative value, i.e.,
– for smaller (I − W ),
– for more negative V (θB ).
• Under this condition, a continuum of separating PBE
exist:


I − W −V (θB ) 
H
.
;
RG
∈ 
θG
∆θ
Pooling Equilibria with No Type Investing
• The bad entrepreneur prefers not to invest iff:
V (θB ) ≤ 0.
• The good entrepreneur prefers not to invest iff:
V (θG) ≤
∆θ
(I − W ).
θB
• This can be rewritten as:
V (θB ) ≤ −
∆θ
W.
θG
• This is stronger than the previous condition.
Pooling Equilibria with Both Types Investing
H
H
• If RB
= RG
= R0H , Bayes Rule pins down the investors’ beliefs:
θ(R0H ) = θ̂.
• Feasibility constraint:
R0H ≤ X H .
(1)
• The good entrepreneur prefers to invest if his project’s
value exceeds the discount:
V (θG) ≥ (θG − θ̂)R0H .
(2)
• He is better off not deviating to any another RH ≥
I−W
θB (i.e., allowing him to raise at least (I − W )) if
the discount is minimum for R0H :
(θG − θ̂)R0H ≤ (θG − θB )
I −W
.
θB
(3)
• The bad entrepreneur prefers to invest if:
−V (θB ) ≤ (θ̂ − θB )R0H .
(4)
• He is always better off not deviating to any another
RH .
• The entrepreneur is able to raise (I − W ) iff
R0H ≥
I −W
.
θ̂
(5)
• Such an equilibrium exists iff:



ν∆θ I
−
V (θB ) ≥ max 
;

θ̂


ν∆θ (I − W ) 
.
−

θB (1 − ν) 
Proof:
• Conditions (1) and (4) are compatible iff V (θ̂) ≥ 0.
V (θB ) ≥ −
ν∆θ I
θ̂
• V (θ̂) ≥ 0 ⇒ Conditions (1) and (5) are compatible.
• V (θ̂) ≥ 0 ⇒ Conditions (2) and (4) are compatible.
• V (θ̂) ≥ 0 ⇒ Conditions (2) and (5) are compatible.
• Conditions (3) and (5) are always compatible.
• Conditions (3) and (4) are compatible iff:
V (θB ) ≥ −
ν∆θ (I − W )
.
θB (1 − ν)
To Summarize
• Recall: V (θG) > 0.
• Separating equilibrium with only good types investing:
V (θB ) ≤ −
∆θ
(I − W ).
θG
• Pooling equilibrium with no investment:
V (θB ) ≤ −
∆θ
W.
θG
• Pooling equilibrium with both types investing:



ν∆θ I
−
V (θB ) ≥ max 
;

θ̂


ν∆θ (I − W ) 
.
−

θB (1 − ν) 
• When a separating equilibrium exists, the Intuitive Criterion eliminates pooling equilibria but not the separating equilibria.
Cho-Kreps Intuitive Criterion
A given PBE violates the Intuitive Criterion if there is
H
H
an out-of-equilibrium move RH ∈
/ {RB
, RG
} and a subset
of types T ⊆ {θB , θG} such that:
i) Any type θ ∈
/ T prefers not to deviate to RH , for all ν
such positive weights are put only on elements of T .
ii) Any type θ ∈ T prefers to deviate to RH , for all ν
such that positive weights are put only on elements of
T.
Intuition: Following a move that type θ would make
under no circumstance, investors’ beliefs should put no
weight on type θ.
An Example
Assumption: W = 0, hence only pooling equilibria
exist.
• Suppose that the good type could choose the equilibrium to be played he would chose RH = 0 or RH = Iθ̂ .











min RH
s.t.

H


θ̂R
≥ I (F) Feasibility







RH ≤ X H (LL) Limited Liability
(1) Under-investment.
• Suppose that the average value is negative, i.e.,
V (θ̂) < 0.
• Credit rationing: Neither type of project is
undertaken. Indeed, there is no feasible repayment
(i.e., RH ≤ X H ) such that investors expect to break
even (Lemon’s Problem).
(2) Over-investment.
• Suppose that the bad project’s value is negative, but
the average value is positive, i.e.,
V (θ̂) > 0 > V (θB ).
• Both types of projects are financed. Indeed,
good entrepreneurs make a profit despite the discount
on claims:
I
θG
θG(X H − RH ) = θG(X H − ) = V (θ̂) > 0.
θ̂
θ̂
• ⇒ Bad firms “pool” with good firms and get financed.
Mitigating Information Asymmetry Problems
Internal funds:
• Suppose that the entrepreneur has W > I.
• No credit rationing: Good projects that would not be
financed externally can be undertaken.
• No bad projects financed: Good entrepreneurs prefer
to self-finance because external finance is more expensive (i.e., claims are sold at a discount) due to pooling
by bad entrepreneurs.
Information-insensitive assets:
• Suppose that the entrepreneur has an asset worth
W > I about which there is no information asymmetry.
• Claims on this asset are sold at their fair price, i.e., no
discount.
• ⇒ The entrepreneur can finance the project.
Reducing the informational gap:
• To convey his type to investors, a good entrepreneur
is willing to pay up to:

I
min (θG − θ̂) ; V (θG) .
θ̂



• Monitoring/Certification: By a bank, venture
capitalist, auditor, etc.
• Signalling: Many Corporate Finance models in specific contexts such as collateral, debt maturity, dividends, IPO underpricing, etc.
– General idea: Good types prove themselves by undertaking an action costly enough to deter mimicking by bad types.
– ⇒ The cost needs to be greater for bad than for
good types.
RISK-BEARING AS A SIGNAL
Leland and Pyle (1977).
Main idea:
• By retaining a large equity stake in their
firms, good entrepreneurs can signal their
type to investors because:
– A large stake is costly (under-diversification).
– It is more costly for worse entrepreneurs,
because of their greater downside risk.
Model
• A risk-averse entrepreneur considers selling part of his
firm’s cash flow claims to risk neutral investors so as
to reduce his risk exposure.
Same model as before except that the entrepreneur:
• already undertook the project at t = 0.
• considers selling some shares at t = 1.
• is risk averse with respect to wealth at t = 2:
– VNM utility function u(X), with u0 > 0 and u00 <
0.
– Normalization: u(0) = 0.
First Best
• By selling a fraction (1 − α) at price P , type θ gets
H
Uθ (α, P ) ≡ θu αX + (1 − α)P + (1 − θ)u ((1 − α)P ) .
• Absent information asymmetry, the price is P = θX H .
• The entrepreneur’s expected utility is maximized for
α = 0 since:
H

0
H
+ (1 − α)θX
∂Uθ (α, θX )
 u αX
= θ(1 − θ)X H 
0
H
∂α
−u (1 − α)θX
< 0 because u00 < 0.
First best:
• The entrepreneur sells his entire stake.
• The investors bear all the risk.
• The entrepreneur is fully insured.
H




Asymmetric Information
• Absent further information, investors are willing to pay
θ̂X H .
• ⇒ An entrepreneur’s utility for selling claims on all
cash flows is
u θ̂X
H
rather than u θX
H
.
• ⇒ “Bad” entrepreneurs are even more eager to sell
claims.
Assumption (**):
u0 (0)
θG(1 − θ̂)
>
.
θ̂ (1 − θG) u0 (X H )
• That is,
∂UθG (α, θ̂X H )
> 0 at α = 1.
∂α
• This implies
∂UθG (α, θ̂X H )
> 0 for all α.
∂α
• ⇒ Good entrepreneurs prefer to retain their claims
and be exposed to risk rather than selling underpriced
claims.
• ⇒ Investors’ rational expectations should reflect that
good types are not selling claims on all cash flows.
• ⇒ This affects the price.
• ⇒ We need to analyze equilibria.
Example:
No Perfect Bayesian Equilibrium with αG = 0
Proof by contradiction. Suppose that αG = 0.
• Given the investors’ beliefs ν (α), they will pay (1 − α) P (α)
for claims on a fraction (1 − α) of the cash flows with:
P (α) = (θB + ν (α) ∆θ ) · X H .
• Good entrepreneurs prefer αG = 0 to α if:
u(P (0)) ≥ UθG (α, P (α)) .
(6)
• Bad entrepreneurs prefer αB to α if:
UθB (αB , P (αB )) ≥ UθB (α, P (α)) .
(7)
• Suppose that αB = 0:
– ⇒ By Bayes’ Rule, ν (0) = ν.
– ⇒ The (ICG) constraint is violated (by Assumption (**)).
• Suppose that αB 6= 0:
– ⇒ By Bayes’ Rule, ν (0) = 1 and ν (αB ) = 0.
– ⇒ By the (ICB ) constraint, UθB (αB , P (αB )) ≥
u θG X H .
– ⇒ P (αB ) ≥ θGX H > θB X H .
– ⇒ ν (αB ) > 0, a contradiction.
Pooling Equilibria?
• Under Assumption (**):
∀α < 1, UθG (1, P ) > UθG α, θ̂X
• ⇒ No pooling equilibrium.
H
.
A Separating Equilibrium
αG = 1.
• αG = 1.
• αB = 0.
• ∀α 6= 1, ν (α) = 0.
• ν (1) = 1.
• Indeed, under Assumption (**)
∂UθG α, θB X
∂α
H
> 0 ∀α.
• Intuition: Retaining shares is a signal of confidence
success.
Other Separating Equilibria
• Suppose that investors view “selling a tiny fraction”
as a signal of good quality.
• The good type will “sell a tiny fraction” since he would
then get:

(1 − α) 
−

∂UθG α, θGX
∂α
H




> 0.
• By mimicking, the bad type would get (almost):
θB u X
H
.
• ⇒ He is better off selling the entire firm and getting:
u(θB X H ) > θB u(X H ).
• ⇒ Expectations are correct, this is a PBE.
How large can (1 − α) be?
• Bad types must prefer to sell the entire firm. Hence,
α must satisfy
H
UθB (0, θB X ) ≥ UθB α, θGX
H
.
• The RHS is strictly decreasing in α.
• The inequality is satisfied for α = 1 and violated for
α = 0.
• ⇒ There exists a unique α∗ ∈ (0, 1) such that LHS=RHS.
• Hence, separation can be sustained for all
αG ≥ α∗ and αB = 0.
Selection with Cho-Kreps
• Puts some constraints on the possible beliefs following
an off-equilibrium move.
• Consider a PBE with α̂ > α∗.
• Suppose the investors observe off-equilibrium move
α = α∗ + ε < α̂.
• Can they “reasonably” believe that the firm is bad?
• The criterion imposes a posterior belief 0 for types
which would never be strictly better off deviating.
• For all ν, the bad type is better-off with αB = 0 than
with any αB > α∗.
• ⇒ The criterion imposes ∀α > α∗, ν(α) = 1.
• But then the good type can always improve on α̂.
• Hence, all equilibria with αG > α∗ are eliminated.
Comments
• Investors require entrepreneurs to invest their own wealth.
• This is inefficient as the entrepreneur bears diversifiable risk.
• Alternative signals that are less costly?
• Retrading? Holding a large stake is a signal only
if one is committed to keeping it. What if the entrepreneur can retrade after the issue? (See Admati,
Pfleiderer and Zechner 1995).
• Model of an entrepreneur going to the market for first
time. However, less readily applied to seasoned offerings.
• (Seasoned) block sale may have quite different motivation and hence informational content.
DEBT AS SIGNAL BY MANAGERS
Ross (1977).
Main idea:
(1) Managerial model:
• Financial distress imposes costs on managers.
• Managers care about market values, not
only fundamentals.
(2) For a given debt level, better firms are less
likely to enter financial distress.
(3) ⇒ Debt is less costly for managers of better firms. ⇒ Can be used as a signal.
Model
Firm run by a manager who:
• Privately knows θ ∈ {θB , θG} .
• Chooses the face value of debt K at t = 0.
• Maximizes (by assumption):
λV0 + (1 − λ) V1 − (K − X)+ ,
where
• λ ∈ (0, 1).
• Vt : Firm’s market value at t.
• (K − X)+: Cost incurred by the manager in financial
distress.
• Note: No uncertainty after t = 1. ⇒ V1 = X.
Debt as a Signal
• Managers of good firms want, to some extent, to convey this type to the market. Since K > X L is costly,
debt might be a signal.
Pooling Equilibria
• Example: K = 0, supported by ν (K) = 0
0.
∀K 6=
• Clearly, K = 0 is the most efficient pooling PBE.
• Good type gets λV (θ̂) + (1 − λ)V (θG).
Separating Equilibria: KG > 0 KB = 0.
• Good type gets V (θG) − (1 − λ) (1 − θG) KG, rather
than λV (θB ) + (1 − λ)V (θG).
• Bad type gets V (θB ), rather than λV (θG) + (1 −
λ)V (θB ) − (1 − λ) (1 − θB ) KG.
• ⇒ Separation requires:
λ∆V
λ∆V
≥ KG ≥
.
(1 − λ) (1 − θG)
(1 − λ) (1 − θB )
• Cho-Kreps
kills all separating
equilibria but the “best”
λ∆V
one KG∗ = (1−λ)(1−θ
) , in which the good type gets:
B
1 − θG 
.
V (θG) − λ∆V 
1 − θB


• If the good type is better off in the “best” separating
than in any pooling PBE, Cho-Kreps selects that PBE,
i.e.,
1 − θG 
∆V .
λ V (θG) − V̂ > λ 
1 − θB


Comments
• Ross’ model is for large firms run by managers who
are not necessarily major shareholders (unlike LP)
• To sustain a separating equilibrium, managers must be
interested in both current (market) value and actual
performance.
– If λ = 1, there is no cost, hence no way to separate.
– If λ = 0, there is no need to separate.
• KG∗ is increasing in λ.
• λ may be interpreted as the intensity of the takeover
threat:
– Benevolent manager: Prevents existing shareholders from selling under-valued stocks (Stein 1988).
– Self-interested manager: Dislikes takeovers.
– Implication: More takeover pressure. ⇒ More
leverage.
• The cost may also be a loss in reputation for the manager.
Note: In Ross (1977), the cost of default is fixed (i.e.,
independent of the shortfall) but cash flows can take more
than two values.
• Profitability and leverage are positively related. Counterfactual.
• Implicit assumption: Managers cannot trade secretly on their own accounts. Otherwise:
– Good types do not signal and buy the stock.
– Bad types signal falsely and short the stock.
• Why use capital structure as a signal? Alternatively,
managers could promise to take a pay cut if performance is poor.
Manager’s objective:
• The manager’s objective is exogenous. However, it
can be motivated as follows. Suppose initially all managers are offered a fixed wage.
λE[V0] + (1 − λ)E[V1] = w.
• After being hired, managers at good firms will want
to signal. They can alter their incentive scheme to
λV0 + (1 − λ) V1 − (K − X)
+
+C
and issue debt X H > K > X L. (Note this is also
in the interest of shareholders of good firm provided
that the constant C is such that total compensation
is not increased).
THE CURSE OF MM
Diversity of Outside Claims?
• MM applies to the claims held by outside investors.
• ⇒ The structure of outside claims is irrelevant.
• Conflicts between insiders and outsiders generate optimal split of cash flows between insiders and outsiders
(e.g. inside equity and outside debt), but not among
outsiders.
• ⇒ Diversity of outside claims cannot be explained:
a mix of diverse outside claims could be merged and
repackaged into identical claims.
• To obtain a theory of the structure of outside claims,
we must (?) take the same way: Consider incentive
and information problems of outside investors (e.g.
incentives to monitor).